Trust-region methods for the derivative-free optimization of nonsmooth black-box functions
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/89470 https://doi.org/10.1137/19M125772X |
Resumo: | In this paper we study the minimization of a nonsmooth black-box type function, without assuming any access to derivatives or generalized derivatives and without any knowledge about the analytical origin of the function nonsmoothness. Directional methods have been derived for such problems but to our knowledge no model-based method like a trust-region one has yet been proposed. Our main contribution is thus the derivation of derivative-free trust-region methods for black-box type functions. We propose a trust-region model that is the sum of a max-linear term with a quadratic one so that the function nonsmoothness can be properly captured, but at the same time the curvature of the function in smooth subdomains is not neglected. Our trust-region methods enjoy global convergence properties similar to the ones of the directional methods, provided the vectors randomly generated for the max-linear term are asymptotically dense in the unit sphere. The numerical results reported demonstrate that our approach is both efficient and robust for a large class of nonsmooth unconstrained optimization problems. Our software is made available under request. |
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Trust-region methods for the derivative-free optimization of nonsmooth black-box functionsNonsmooth optimization, derivative-free optimization, trust-region-methods, black-box functions.In this paper we study the minimization of a nonsmooth black-box type function, without assuming any access to derivatives or generalized derivatives and without any knowledge about the analytical origin of the function nonsmoothness. Directional methods have been derived for such problems but to our knowledge no model-based method like a trust-region one has yet been proposed. Our main contribution is thus the derivation of derivative-free trust-region methods for black-box type functions. We propose a trust-region model that is the sum of a max-linear term with a quadratic one so that the function nonsmoothness can be properly captured, but at the same time the curvature of the function in smooth subdomains is not neglected. Our trust-region methods enjoy global convergence properties similar to the ones of the directional methods, provided the vectors randomly generated for the max-linear term are asymptotically dense in the unit sphere. The numerical results reported demonstrate that our approach is both efficient and robust for a large class of nonsmooth unconstrained optimization problems. Our software is made available under request.Society for Industrial and Applied Mathematics2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/89470http://hdl.handle.net/10316/89470https://doi.org/10.1137/19M125772Xeng1052-62341095-7189https://epubs.siam.org/doi/abs/10.1137/19M125772XLiuzzi, GiampaoloLucidi, StefanoRinaldi, FrancescoVicente, Luís Nunesinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2022-05-25T06:21:19Zoai:estudogeral.uc.pt:10316/89470Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:09:46.337668Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions |
title |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions |
spellingShingle |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions Liuzzi, Giampaolo Nonsmooth optimization, derivative-free optimization, trust-region-methods, black-box functions. |
title_short |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions |
title_full |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions |
title_fullStr |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions |
title_full_unstemmed |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions |
title_sort |
Trust-region methods for the derivative-free optimization of nonsmooth black-box functions |
author |
Liuzzi, Giampaolo |
author_facet |
Liuzzi, Giampaolo Lucidi, Stefano Rinaldi, Francesco Vicente, Luís Nunes |
author_role |
author |
author2 |
Lucidi, Stefano Rinaldi, Francesco Vicente, Luís Nunes |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Liuzzi, Giampaolo Lucidi, Stefano Rinaldi, Francesco Vicente, Luís Nunes |
dc.subject.por.fl_str_mv |
Nonsmooth optimization, derivative-free optimization, trust-region-methods, black-box functions. |
topic |
Nonsmooth optimization, derivative-free optimization, trust-region-methods, black-box functions. |
description |
In this paper we study the minimization of a nonsmooth black-box type function, without assuming any access to derivatives or generalized derivatives and without any knowledge about the analytical origin of the function nonsmoothness. Directional methods have been derived for such problems but to our knowledge no model-based method like a trust-region one has yet been proposed. Our main contribution is thus the derivation of derivative-free trust-region methods for black-box type functions. We propose a trust-region model that is the sum of a max-linear term with a quadratic one so that the function nonsmoothness can be properly captured, but at the same time the curvature of the function in smooth subdomains is not neglected. Our trust-region methods enjoy global convergence properties similar to the ones of the directional methods, provided the vectors randomly generated for the max-linear term are asymptotically dense in the unit sphere. The numerical results reported demonstrate that our approach is both efficient and robust for a large class of nonsmooth unconstrained optimization problems. Our software is made available under request. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/89470 http://hdl.handle.net/10316/89470 https://doi.org/10.1137/19M125772X |
url |
http://hdl.handle.net/10316/89470 https://doi.org/10.1137/19M125772X |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1052-6234 1095-7189 https://epubs.siam.org/doi/abs/10.1137/19M125772X |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799133992906129408 |